Paul Horwich (1998), following a number of others, proposes a schematic compositional format for the specification of the meanings of complex expressions. The format is schematic in the sense that it identifies grammatical schemata that do not presuppose any particular account of primitive word meanings: whatever the nature of meanings, the application of the schemata to them will serve to explain compositionality. This signals, for Horwich, that compositionality is a non‐substantive constraint on theories of meaning. Drawing on a range of linguistic data, the present paper argues that while the bare idea of compositionality indeed does not presuppose any account of meaning, Horwich's format is empirically inadequate. The argument here goes back to Chomsky's early position on the descriptive inadequacy of rewrite grammars and the consequent need for transformations. It will also be seen that the data militates for a general claim that meaning relevant structure is projected from words rather than imposed on them schematically. Finally, it will be indicated how this reasoning from syntactic considerations is flush with a more traditional philosophical understanding of compositionality.